\draw[name path=g1,Azure4] (A)--(\$(A)!2.1cm!(C)\$);
\draw[name path=g2,Azure4] (A)--(\$(A)!2.1cm!(D)\$);
\path [name intersections={of = L1 and g1, by={E}}];
\path [name intersections={of = L1 and g2, by={F}}];